La formula di Ewens-Pitman nell'inferenza bayesiana non parametrica di specie rare

In Bayesian nonparametrics the role of the parameter appearing in a statistical model is taken by a probability distribution; therefore, the parameter space becomes a class of probability distributions defined on a given sample space. A Bayesian usually considers the class of all probability measures on the sample space and defines a probability on this class, the so-called prior distribution. In this work a particular tailfree random probability measures, termed Dirichlet process, is presented. In particular, the Dirichlet process is characterized by the double advantage of having a large support, with respect to a suitable topology on the space of probability measures on the sample space, and of being analytically manageable for Bayesian posterior computations. Since the introduction of the Dirichlet process, the literature on Bayesian nonparametrics has grown enormously and need for solutions of new problems has caused the introduction of new prior distribution.